Growth of Massive Black Holes at Their Late Stage

It is believed that the growth of local massive black holes was dominated by accretion during quasar phases, while a fraction of the local black hole mass was accumulated through accreting gases at very low rates. We derive the black hole mass density as a function of redshift with the bolometric luminosity function of active galactic nuclei (AGNs) assuming that massive black holes grew via accreting the circumnuclear gases, in which the derived black hole mass density is required to match the measured local black hole mass density at z = 0. Advection-dominated accretion flows (ADAFs) are supposed to be present in low-luminosity AGNs/normal galaxies, which are very hot and radiate mostly in the hard X-ray band. Most of the X-ray background (XRB) is contributed by bright AGNs, and a variety of AGN population synthesis models were developed to model the observed XRB in the last two decades. Based on our derived black hole mass density, we calculate the contribution to the XRB from the ADAFs in faint AGNs/normal galaxies with a given Eddington ratio distribution, which is mostly in the hard X-ray energy band with an energy peak at ~200 keV. The growth of massive black holes during the ADAF phase can therefore be constrained with the observed XRB. Combining an AGN population synthesis model with our results, we find that the fitting on the observed XRB, especially at the hard X-ray energy band with gsim100 keV, is improved provided the contribution of the ADAFs in low-luminosity AGNs/normal galaxies is properly included. It is found that less than ~15% of local massive black hole mass density was accreted during ADAF phases. We suggest that more accurate measurements of the XRB in the energy band with gsim100 keV in the future may help constrain the growth of massive black holes at their late stage. We also calculate their contribution to the extragalactic γ-ray background (EGRB), and find that less than ~1% of the observed EGRB is contributed by the ADAFs in these faint sources.